Estimation of Beta in a Simple Functional Capital Asset Pricing Model for High Frequency US Stock Data

This project applies the methods of functional data analysis (FDA) to intra-daily returns of US corporations. It focuses on an extension of the Capital Asset Pricing Model (CAPM) to such returns. The CAPM is essentially a linear regression with the slope coefficient . Returns of an asset are regressed on index return. We compare the estimates of obtained for the daily and intra-daily returns. The variability of these estimates is assessed by two bootstrap methods. All computations are performed using statistical software R. Customized functions are developed to process the raw data, estimate the parameters and assess their variability. The results turn out to be: First, the estimates of obtained for the intradaily returns have bigger absolute values than those for the daily returns; secondly, to assess the variability of the estimates of obtained for the intra-daily returns, residual bootstrap method is more reliable than pairwise bootstrap method; thirdly, the estimates of obtained for the intra-daily returns are much higher in absolute values in 2004 than those in any other years. 1